Camera calibration: adjusting camera lense edge distortion¶
by Uki D. Lucas
Motivation¶
The raw camera data usually has a certain level of distortion caused by lense shape, this is especially pronounced on the edges of the image. The correction is essential in applications like image recognition where mainitaining the shape is essential, especially in autonomous vehicles, robotics and even in 3D printing.
Solution approach¶
The common solution is to compare a known shape object e.g. a chessboard with the image taken, then calculate this specific camera's adjustment parameters that then can be applied to every frame taken by the camera. If the camera changes (camera lense type, resolution, image size) in the set up, the new chessboard images have to be taken and calibration process repeated.
The angle of chessboard in relation to the camera does not matter, in fact the sample pictures should be taken from various angles. Only the pictures with whole chessboard showing will work.
You should take many, at least 20 sample images, any less and the learning process renders images that are not a well corrected.
Desired result (spoiler alert!)¶
For people who have no patience to read the whole paper I am including the final result:
import numpy as np # used for lists, matrixes, etc.
import cv2 # we will use OpenCV library
%matplotlib inline
# If executing this file, set to True, if using as library, set to False
should_run_tests_on_camera_calibration = True
Useful helper method¶
def plot_images(left_image, right_image):
import numpy as np
import matplotlib.pyplot as plt
plt.figure(figsize=(20,10))
plot_image = np.concatenate((left_image, right_image), axis=1)
plt.imshow(plot_image)
plt.show()
def __get_sample_gray(image_file_name: str):
import cv2 # we will use OpenCV library
image_original = cv2.imread(image_file_name)
# convert BGR image to gray-scale
image_gray = cv2.cvtColor(image_original, cv2.COLOR_BGR2GRAY)
return image_original, image_gray
The pattern will look for "inner corners" e.g. black touching the black square¶
def __find_inside_corners(image_file_names: list, nx: int=9, ny: int=6, verbose = False):
# Chessboard dimentsions
# nx = 9 # horizontal
# ny = 6 # vertical
import cv2 # we will use OpenCV library
import numpy as np
# Initialise arrays
# Object Points: points on the original picture of chessboard
object_point_list = []
#Image Points: points on the perfect 2D chessboard
image_points_list = []
# Generate 3D object points
object_points = np.zeros((nx*ny, 3), np.float32)
object_points[:,:2] = np.mgrid[0:nx, 0:ny].T.reshape(-1, 2)
#print("first 5 elements:\n", object_points[0:5])
# see: http://docs.opencv.org/trunk/dc/dbb/tutorial_py_calibration.html
termination_criteria = (cv2.TERM_CRITERIA_EPS + cv2.TERM_CRITERIA_MAX_ITER, 30, 0.001)
chessboard_dimentions = (nx, ny)
import matplotlib.pyplot as plt
for image_file_name in image_file_names:
if verbose:
print("processing image:", image_file_name)
image_original, image_gray = __get_sample_gray(image_file_name)
# Find the chess board corners
# Paramters:
# - image_gray
# - the chessboard to be used is 9x6
# - flags = None
has_found, corners = cv2.findChessboardCorners(image_gray, chessboard_dimentions, None)
if has_found == True:
# fill in ObjectPoints
object_point_list.append(object_points)
corners2 = cv2.cornerSubPix(image_gray, corners, (11,11), (-1,-1), termination_criteria)
# fill in ImagePoints
image_points_list.append(corners2)
# Draw and display the corners
# I have to clone/copy the image because cv2.drawChessboardCorners changes the content
image_corners = cv2.drawChessboardCorners(
image_original.copy(),
chessboard_dimentions,
corners2,
has_found)
if verbose:
plot_images(image_original, image_corners)
else: # not has_found
if verbose:
print("The", chessboard_dimentions,
"chessboard pattern was not found, most likely partial chessboard showing")
plt.figure()
plt.imshow(image_original)
plt.show()
# end if has_found
# end for
return object_point_list, image_points_list
Calibrate using points¶
def prep_calibration(image_file_names: list, use_optimized = True, verbose = False):
import cv2 # we will use OpenCV library
# find CORNERS
object_point_list, image_points_list = __find_inside_corners(image_file_names)
# get smaple image, mostly for dimensions
image_original, image_gray = __get_sample_gray(image_file_names[1])
# Learn calibration
# Returns:
# - camera matrix
# - distortion coefficients
# - rotation vectors
# - translation vectors
has_sucess, matrix, distortion, rvecs, tvecs = cv2.calibrateCamera(
object_point_list,
image_points_list,
image_gray.shape[::-1],
None,
None)
## I can use this to improve the calibration (no cropped edges, but curved edges)
image_dimentions = image_original.shape[:2] # height, width
matrix_optimized, roi = cv2.getOptimalNewCameraMatrix(
matrix,
distortion,
image_dimentions,
1,
image_dimentions)
return matrix, matrix_optimized, distortion
def apply_correction(
image_file_name: str = None,
matrix = None,
distortion = None,
matix_optimized = None): # optional
import cv2 # we will use OpenCV library
print("Removing distortion in", image_file_name)
image = cv2.imread(image_file_name)
image_corrected = cv2.undistort(image, matrix, distortion, None, matix_optimized)
if matix_optimized is None:
print("NOT OPTIMIZED: edges are cropped.")
else:
print("OPTIMIZED: fuller image, but with edge distortion.")
plot_images(image, image_corrected)
return image_corrected
Get list of sample chessboard images by this camera¶
if should_run_tests_on_camera_calibration:
# read a list of files using a parern
import glob
image_file_names = glob.glob("camera_cal/calibration*.jpg") # e.g. calibration19.jpg
print("found", len(image_file_names), "calibration image samples" )
print("example", image_file_names[0])
#if should_run_tests_on_camera_calibration:
# object_point_list, image_points_list = find_inside_corners(image_file_names)
if should_run_tests_on_camera_calibration:
matrix, matrix_optimized, distortion = prep_calibration(image_file_names, use_optimized = True)
Remove the distortion form the images¶
if should_run_tests_on_camera_calibration:
image_file_name = "test_images/test1.jpg"
image_corrected = apply_correction(image_file_name, matrix, distortion)
image_corrected = apply_correction(image_file_name, matrix, distortion, matrix_optimized)
# save to disk
cv2.imwrite("output_images/" + "optimized_" + image_file_name, image_corrected)
if should_run_tests_on_camera_calibration:
for image_file_name in image_file_names:
import cv2 # we will use OpenCV library
image_corrected = apply_correction(image_file_name, matrix, distortion)
image_corrected = apply_correction(image_file_name, matrix, distortion, matrix_optimized)
# save to disk
cv2.imwrite("output_images/" + "optimized_" + image_file_name, image_corrected)
Conclusion¶
The optimized image provides a better camera calibration because it maintains more area of the image instead of cropping it. This is especially visible in the example below. I have manually drawn the red lines to show the straightness of on the corrected image on the right. The edge curvature plays mental/optical trics.
I could improve even further if I took more chessboard samples.
The final image might be cropped to hide the curved edges.